Affiliation:
1. Indian Institute of Technology, Kanpur, India
Abstract
We give a simple and new randomized primality testing algorithm by reducing primality testing for number
n
to testing if a specific univariate identity over
Z
n
holds.We also give new randomized algorithms for testing if a multivariate polynomial, over a finite field or over rationals, is identically zero. The first of these algorithms also works over
Z
n
for any
n
. The running time of the algorithms is polynomial in the size of arithmetic circuit representing the input polynomial and the error parameter. These algorithms use fewer random bits and work for a larger class of polynomials than all the previously known methods, for example, the Schwartz--Zippel test [Schwartz 1980; Zippel 1979], Chen--Kao and Lewin--Vadhan tests [Chen and Kao 1997; Lewin and Vadhan 1998].
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference26 articles.
1. On Distinguishing Prime Numbers from Composite Numbers
2. Agrawal M. Kayal N. and Saxena N. 2002. PRIMES is in P. Annals of Math. to appear. Update available at http://www.cse.iitk.ac.in/users/manindra/primality.ps. Agrawal M. Kayal N. and Saxena N. 2002. PRIMES is in P. Annals of Math. to appear. Update available at http://www.cse.iitk.ac.in/users/manindra/primality.ps.
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